Answer: The temperature of the object after one hour is 12.9°C to the nearest tenth of a degree
Step-by-step explanation:
Please see the attachments below
Answer:
12.9 degree C
Step-by-step explanation:
1 hour = 60 minutes
So the Newton's law of cooling state that the rate of changing in temperature is proportional to the different in temperature, in other words:
[tex]\frac{dT}{dt} = -k(T - T_e)[/tex]
where t is the time in minute, k is the cooling constant and [tex]T_e = 4^o C[/tex] is the environmental temperature. This differential equation can be solved to have a form of
[tex]T(t) = T_e + (T_0 - T_e)e^{-kt}[/tex]
where [tex]T_0 = 21^o C[/tex] is the initial temperature.
We know that at 25 minutes T(25) = 17
[tex]4 + (21 - 4)e^{-25k} = 17[/tex]
[tex]4 + 17e^{-25k} = 17[/tex]
[tex]e^{-25k} = (17 - 4)/17 = 0.765[/tex]
[tex]-25k = ln(0.765) = -0.268[/tex]
[tex]k = -0.268 / -25 = 0.0107[/tex]
So after 60 minutes:
[tex]T(60) = 4 + 17e^{-0.0107*60} = 4+17*0.525 = 12.9 ^o C[/tex]
